Different Senses of the Quantifers?

Carnapians want to say that different things can be truely said to exist when speaking in different language-frameworks. So the existential quantifier "Ex" will mean different things in these different frameworks. But can there really be multiple different meanings for these different uses of Ex, which would qualify as different kinds of e.g. existential quantification?

An argument that you can't is: The meaning of Ex is determined by its introduction and elimination rules. So any putative kind of existential quantifier would need to obey them. Hence different senses E1 and E2 from different frameworks would both have to obey the standard introduction and elimination rules for Ex. But if E1 and E2 obey these rules, then you can prove E1x from E2x and vice versa. Hence there is no room for ambiguity.

This argument can't be right though, if restricted quantification ('There is nothing in the fridge'. 'All the beers are in the fridge') - something that even the most ardent anti-Carnapians accept- counts as `a kind of' quantification. And intuitively it is. Hence in order to seem like a kind of quantification, a connective need not obey the full introduction rules. It suffices if there's a more limited range of instances of the introduction schema
P(x) --> Ex P(x) that speakers accept, together with all corresponding instances of the elimination schema Ex P(x). (A^B^C..^P(z) > F) ---> F (in cases where z does not occur free in A,B, C... or F). This is what we have for beers in the fridge.

Why can't the Carnapian claim that the same thing goes on with different linguistic frameworks? The different choices for when P(x) --> E2x P(x) is acceptable will each correspond to a different meaning for the existential quantifier. We can even formally represent these different possible senses for existential quantification formally, by saying a kind of existential quantification E_i corresponds to each subset S_i of the set of predicate-expressions (i.e. to each choice of what predicate-expressions the introduction and elimination schema are supposed to hold for).

You are probably worrying that this turns the Carnapian into a kind of maximalist (all the objects in question really exist, different frameworks just correspond to different framework restrictions) but I can't actually see any argument for that. So speak up if you can!

Species and Couches

A smart philosopher of biology I know claims to be researching "whether there are (really) species, as opposed to just individuals". So far as I can tell, he is investigating whether biological explanations that appeal to species are not really always better put in terms of individuals. That is, he's studying whether talking about species serves a certain kind of (ineliminable?) role in biological explanation.

That definitely seems worth worth investigating - especially since there are so many cases where the distinction between different species looks very unprincipled. (Because of ring species and ligers it won't do to just say that two things are the same species if they can produce fertile offspring.)

But it seems strange to me that he puts this in terms of `investigating whether species really exist'. This is because, presumably, he thinks couches really exist, and yuppies too, even though we could surely phrase an adequate biological and scientific theory in such a way as not to entail any sentences of the form Ex couch (x) or Ex yuppie(x).

What I THINK might be going on is that he thinks objects need to earn their keep, in a way that concepts don't. That is: it's fine to apply scientifically useless predicates like "...is a yuppie", but not to introduce scientifically useless *objects* like species. On this reading he would be fine with saying that dogs exist, or that two newts are consepecifics, but not with saying that there are (abstract) objects called species.

But I don't see quite how one would motivate this differential treatment. (Admittedly this may have something to do with my current adherence to the merely logical notion of objecthood). Also, the problems for the notion of species looking unprincipled seem to apply just as much to claims about being a dog or being two animals being conspecific.

*Obviously some scientifically useless objects are bad to introduce, like the flying spagetti monster but that's because their existence would entail false claims about the distribution of matter in space-time. In contrast, just proposing new ways to think of the same old distribution of matter etc. in space-time as constiuting objects e.g. (tables, vs. half tables, vs. complete livingroom sets vs. dearths of tables) in different ways, seems harmless.

[edit: there is something SLIPPERY about the way I am using the concept/object distinction here. must think more about this, and ask the philosopher of bio]

Thin Realism #2

Hmm on further reflection, `thin realism' is just Lumpism.

So see the essay above for why Lumpism is right and all that seductive stuff about the world having a logical structure/existence claims having a special epistemological status is wrong.

"Thin Realism" - what could it be?

I always want to say "I think there are numbers - but I understand existence in a thin logical sense". But I feel kindof dishonest saying this. It's too much like the sleazy "Of course P - but I don't mean that in any deep philosophical way" which happens when Wittgensteinians get lazy.

So here are some actual concrete ways in which I differ from other platonists (i.e. other people who believe there are mathematical objects).

1. I don't think we need to posit numbers to explain how there can be unknowable mathematical facts.

2. I think fictionalism/if-then-sim is is perfectly coherent. We could have had a mathematical practice which was completely based around mathematical properties, and studying their relaitons to one another e.g.: `Insofar as anything heirarchy-of-sets-izes, it's mathematically necessary that it satisfies the contiuum hypothesis'.

And here's an attempt to say what having only "a thin logical notion of existence" means:

When we ask what objects exist, this is equivalent to asking what sentences with a given logical form (Ex) Fx are true. So far, this is just Quinean orthodoxy.

But now the question is: what makes a given sentence (say, of English) have a certain logical form?

Now, I think having existential form is just a matter of what inferences can be made with that sentence, and what other -contrasting- sentences are in the language. We cook up various logical categories in order to best represent, and exploit, patterns in which inferences are truth preserving. Furthermore, there's noting special about objects, and object expressions. Each component of a sentence (be it concept-word, object-word, connective or opporator) makes a systematic contribution to the truth conditions of the sentences it figures in (i.e. the class of possible situations where the sentence is true).

On this view, choices about the logical form of a sentence wind up not being very deep - the question is just what's the most elegant way to capture certain inference relations.

In contrast, (I propose) having a "thick" notion of objecthood and existence, means thinking that there IS something more than elegant summary of inference relations at stake when we decide how to cut sentences up into concepts and objects. For example, you might think

1. It's easy to learn statements which don't imply that any objects exist (all bachelors are unmarried), whereas learning statements that do imply the existence of at least one object (there are some bachelors) is harder.

2. The *world* has a logical structure too! - so the most elegant way of cutting up your sentences to capture inference relations might still be wrong, because it fails to respect the logical structure of the world.

[Oh yes, they are kindof seductive. More about why they are wrong later.]